We have often heard the expression “You can’t prove a negative.”  Such an axiom stems from the principle that to prove something you need only show one example of it, while proving its non-existence would require looking everywhere, which would be impossible.  Consequently, there is some truth to the statement.  Asking Saddam Hussein to prove he didn’t have weapons of mass destruction, would have placed an impossible task on him, while proving he had WMD would have required only showing an example of one. The proof may still be difficult, but not conceptually impossible.

 The axiom is in fact true for most circumstances.  It would be -- generally speaking -- more difficult to disprove any assertion than to prove it.  However, the burden of proof always lies upon the one making the assertion -- but that’s a different issue and involves another rule of logic which states that: “In the absence of compelling evidence non-belief is preferred.” 

 The problem is the axiom is vague and does not address particular situations, thus it cannot be a true axiom because it is not always true.  The issue here is really one of “universality,” not positiveness or negativeness.  Saying “I believe all planets have gravity” is a universal positive statement and is also not provable, due to the impossibility of examining all planets.  If I were to say “I don’t have a million dollars in my bank account” this could easily be proven though it is a negative, just by looking.  It just all depends upon the universality of the calm.  The axiom should really be stated as, “You can’t prove a universal assertion.”  

Claiming there is a God is not a universal claim, thus its proof should be easier than saying “There is no God,” which is a universal claim and is simply impossible to prove empirically (using direct evidence).  How can one prove there is no such thing as a supernatural being somewhere in or outside of the universe?  We just can't check all places for its nonexistence, and would we even know what to look for?  Of course, again, the burden of proof lies upon the believer, not the disbeliever, and one could argue that since the proof should be possible, while disproof is impossible, then why haven’t you proven it yet?  Your lack of proof tends to show it isn’t true.

You absolutely cannot prove there is no Santa Clause, because you cannot look everywhere to demonstrate he doesn't exist.  Yes, we know there is no Santa Clause because we know he was invented out of fantasy.  But, there would be no way of actually disproving his existence if we did not already know that he did not exist.  People could just rationalize forever, saying, “Well he gets sick every Christmas and doesn’t always deliver gifts to every house, but we think he used to hundreds of years ago.”

You cannot disprove the Tooth Fairy, even if you know your mother puts the money under your pillow.  Maybe there really are tooth fairies somewhere else.  You can’t look for and examine everywhere for an absence of tooth fairies; the possibility of their being invisible would make the task even more difficult!

The same problem exists with the Lock Ness Monster, Big Foot, Crop Circles, etc.  These things catch on because you can’t disprove there’s a monster in Lock Ness unless the drain the Lock.  You can’t prove there’s no Big Foot unless you search every square inch forest in the world, and you can disprove aliens make crop-circles because you can’t watch every field every night all over the world, and you can’t go back in time to watch the fields where crop-circles were made.  Yes, people have admitted to making the circles, someone admitted to even making the Big-Foot costume and someone admitted attaching a toy Plesiosaur to a miniature submarine and photographed, but even with that we cannot be 100 percent certain from a purely logical standpoint that such things do not actually exist. 

“You Can’t Prove a Negative” gets its steam from the fact that most assertions are not universals, while the opposing counterclaims virtually always must be universals.

Let take a look at the opposite situation:

“An apple a day, keeps the doctor away,” is a universal positive claim, and thus cannot be proven, but doesn't need to be because it is obviously not always true..

“An apple a day, doesn’t keep the doctor away,” is negative, but not a universal statement; and can easily be proven by finding just one person who got sick and required a doctor, even after eating an apple.  Of course such a statement is a maxim, not an axiom and is just meant to teach that eating apples is healthy.

The above show us how much more difficult it is it to make a universal claim.  Most universal claims can easily be shown to not be necessarily true, thus universal assertions are more rare than universal denials, rendering a statement like "You can't prove a positive" to not become popularized as its counterpart "You can't prove a negative" has. 

It the end, it's just all really about how universal the claim is, that’s all.

I hope I have cleared this issue up.

Brother Mark

Church of Rationality

http://rational-church.com